Interval approach to braneworld gravity

Abstract

Gravity in five-dimensional braneworld backgrounds may exhibit extra scalar degrees of freedom with problematic features, including kinetic ghosts and strong coupling behavior. Analysis of such effects is hampered by the standard heuristic approaches to braneworld gravity, which use the equations of motion as the starting point, supplemented by orbifold projections and junction conditions. Here we develop the interval approach to braneworld gravity, which begins with an action principle. This shows how to implement general covariance, despite allowing metric fluctuations that do not vanish on the boundaries. We reproduce simple ${\mathbf{Z}}_{\mathbf{2}}$ orbifolds of gravity, even though in this approach we never perform a ${\mathbf{Z}}_{\mathbf{2}}$ projection. We introduce a family of ``straight gauges'', which are bulk coordinate systems in which both branes appear as straight slices in a single coordinate patch. Straight gauges are extremely useful for analyzing metric fluctuations in braneworld models. By explicit gauge-fixing, we show that a general $\mathrm{Ad}{\mathrm{S}}_{5}/\mathrm{Ad}{\mathrm{S}}_{4}$ setup with two branes has at most a radion, but no physical ``brane-bending'' modes.